Question

If the $(2p)^{th}$ term of a H.P. is $q$ and the $(2q)^{th}$ term is $p$, then the $2(p + q)^{th}$ term is-

• A. $\frac{pq}{2(p + q)}$
• B. $\frac{pq}{p + q}$
• C. $\frac{2pq}{p + q}$
• D. $\frac{p + q}{pq}$

Answer 1

The Correct Option is D

If $a$ is the first term and $d$ is the common difference of the associated A.P.
$\frac{1}{q} = \frac{1}{a} +\left(2p-1\right)d, \frac{1}{p} = \frac{1}{a} +\left(2q-1\right)d $
$\Rightarrow d = \frac{1}{2pq} $
If $h$ is the $ 2\left(p+q\right)^{th} $ term $ \frac{1}{h}=\frac{1}{a} + \left(2p + 2q - 1\right)d$
$ = \frac{1}{q} + \frac{1}{p} = \frac{p+q}{pq} $